Summary in English
Within the frame of the research project ARK&APP (2013–2015) two quantitative surveys and 12 qualitative case studies are conducted. The present case study is the second of three case studies in mathematics.
In this study we follow an upper secondary school class of 21 students and their teacher in 1T mathematics in the general studies program working with algebra. We observed them through 7 lessons spread over 3 weeks in September 2014. The data includes pre- and post-tests evaluating students’ learning outcomes, observations and video recordings of various forms of classroom interactions as well as the interviews with the students of the focus group and the teacher. Three research questions guide the study:
- How are educational resources used in teaching practices?
- What role do various educational resources play in interactions between students and their teacher?
- How do educational resources foster engagement and learning among students?
The results show that whole-class teaching and individual work are dominating activities. Whole-class teaching consisted mostly of discussions where the teachers problematized themes, which gave the students the possibility to express and discuss different ways of thinking mathematically. The teacher also spent time on lecturing when introducing new themes within algebra. In whole-class teaching he mainly used the whiteboard and to a certain extent textbooks. When students worked individually they mainly used their textbook with tasks and notebooks but also digital learning resources such as GeoGebra and Graph. Their teacher would then guide them in interpreting and solving their tasks.
The teacher's intention was through use of various educational resources and representations to illustrate alternative ways to think mathematically. The students applied various methods for similar tasks, and the teacher used visualizations on the whiteboard to problematize concepts. When the students worked individually or in pairs with learning resources they spent considerable time on validating their solutions − mainly by checking the correct answer provided on the last pages of the textbook or by considering their peer's solutions. The teacher was notified if a student repeatedly got the incorrect answer.
The students were focused and engaged throughout the period. They concentrated on their tasks and participated actively in discussions initiated by their teacher. The digital learning resources provided more dynamic interactions and more engagement between the students. However, we cannot determine whether the students had significant learning outcomes from pre- to post-tests.
The most prominent characteristic of this case study is how the teacher insisted on mediating the students' mathematical understanding. In line with principles and standards for mathematical teaching (NCTM, 2014) the teacher emphasized productive disposition, conceptual understanding and adaptive reasoning. In whole-class teaching he challenged the students to reason, discuss and collaboratively solve tasks. When students worked individually the teacher facilitated them in trying out different methods and representations for similar tasks. Such competencies are important in terms of flexibility in solution strategies, deep procedural knowledge and conceptual understanding underlying mathematical procedures. Variation in use of educational resources provides different lenses to understand the subject matter and plays an important part in terms of conceptual development and deep mathematical understanding.